Journal article
A gap in the achievable radio number line
AKCE international journal of graphs and combinatorics, Vol.10(4), pp.349-357
01/01/2013
DOI: 10.1080/09728600.2013.12088751
Abstract
Let d(u, v) denote the distance between two distinct vertices of a connected graph G, and diam(G) be the diameter of G. A radio labeling c of G is an assignment of positive integers to the vertices of G satisfying d(u, v) + |c(u) - c(v)| ≥ diam(G) + 1. The maximum integer in the range of the labeling is its span. The radio number of G, rn(G), is the minimum possible span. We show that the path on n vertices, P
n
, achieves the maximum possible radio number. We then ask whether any integer in the range [n, rn(P
n
)] fails to be the radio number of some connected graph of order n, and answer this question in the affirmative.
Details
- Title: Subtitle
- A gap in the achievable radio number line
- Creators
- Diana Canales - Universidad Autónoma del Estado de HidalgoMaggy Tomova - University of IowaCynthia Wyels - Mathematics CSU Channel Islands One University DrJ Gallian
- Resource Type
- Journal article
- Publication Details
- AKCE international journal of graphs and combinatorics, Vol.10(4), pp.349-357
- Publisher
- Taylor & Francis
- DOI
- 10.1080/09728600.2013.12088751
- ISSN
- 0972-8600
- eISSN
- 2543-3474
- Language
- English
- Date published
- 01/01/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9984240774302771
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